Write down your own verbal description for a dynamical system, and write down the equations for...

Write down your own verbal description for a dynamical system, and write down the equations for the dynamical system. (It is fine if this system is very simple! It is also fine if the scenario is not very realistic, as long as the equations match the description!)

Expert Solution

$$A dynamical system is any system, man-made, physical, or biological, that changes in time. To study any system with the help of tools of dynamical system we need to nd out what is the ``something" that will evolve over time and what is the rule that speci es how that something evolves with time.$

$$Consider an example where you deposit some amount $P_0$ at an interest of $10\%$per annum. Amount after one year will $P_1=P_0+0.1P_0=1.1P_0$ \\ similarly $P_2=P_1+0.1P_1=1.1P_1=1.1 ^2*P_0$ \\ $=P_n=1.1^n*P_0$ \\ Now to consturct a dynamical system out of it consider the function \\$f(x)=1.1*x$ Then amount after n years is given by $f^n(x)$ which is f composed with itself n times$

Consider an example where you deposit some amount P

A dynamical system is any system, man-made, physical, biological, or that changes in time. To study any system with the help of tools of dynamical system we and what is the rule that speci es how that something evolves with time need to nd out what is the "something" that will evolve over time

example where you deposit Consider an some amount P at an interest of 10%per annum. Amount after one year will Pi Po0.1Po 1.1P similarly P2 P0.1P1 1.1P1 1.12 Po - P= 1.1 Po Now to consturct a dynamical system out of it consider the function f(x)1.1 Then amount after n years is given by f (x) which is f composed with itself n times

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Colby Messinger answered 1 year ago

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